\documentclass[10pt]{article} % required
\pagestyle{empty} % required
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{color}
\usepackage[T1]{fontenc}

\begin{document}\definecolor{fgC}{rgb}{0,0,0}\color{fgC}\[\begin{matrix}
 U_t = R(U)  \\ 
 U = \begin{bmatrix}
 v_1 \\ 
 v_2 \\
 v_3
 \end{bmatrix}\;\;\;
 R(U) = \begin{bmatrix}
 \sigma (v_2-v_1) \\ 
 v_1(\rho - v_3) -v_2 \\
v_1 v_2 - \beta v_3
 \end{bmatrix} 
\end{matrix}\]\end{document}